There are no plans to alter England’s regulations and sources say the other nations are “unlikely to change”.
The plans for 23-27 December will be discussed in a call between officials.
It comes as London, much of Essex and parts of Hertfordshire moved into tier three restrictions overnight.
Around 61% of England’s population is now living under the toughest rules.
Cabinet Office minister Michael Gove will resume talks with leaders of the devolved administrations on Wednesday morning amid warnings hospitals could become overwhelmed if the easing of Covid regulations across the UK continue as planned.
The rules will allow up to three households to form a bubble and stay overnight at each other’s homes over a five-day period.
Labour has called for the measures over Christmas to be toughened, while two leading journals said the “rash” decision to ease restrictions would “cost many lives”.
In a joint editorial, the British Medical Journal and Health Service Journal stressed that demand on the NHS was increasing, adding that a new strain of coronavirus – identified in both England and Wales – “has introduced further potential jeopardy”.
But instead of a change to the rules, advice around celebrating Christmas safely across the UK is expected to be significantly strengthened.
People will be urged to stay local where possible and to think carefully about who they bubble with, such as avoiding the elderly or at-risk relatives.
An information campaign is expected to be launched in the days running up to Christmas.
After the first round of talks on Tuesday, a UK government source said they were “keen to maintain a UK-wide approach”.
On Tuesday, Scotland’s First Minister, Nicola Sturgeon, argued there was a “case” for tightening the planned freedoms to combat a rise in infections.
Wales’s First Minister, Mark Drakeford, said “the choice is a grim one”, but the current plans were a “hard-won agreement” he would not put aside “lightly”.
Despite the significant pressure for a rethink, leaders from the UK are likely to stick to the deal they agreed last month.
There are no plans for a rethink of regulations in England – and it’s unlikely Wales, Northern Ireland and Scotland will make changes either.
But there are real concerns among decision makers about the impact the relaxations could have – in particular the number of people who will be travelling across the UK.
So you can expect to hear much stronger advice that just because you can mix, that doesn’t mean you should.
Ministers are preparing to warn people they should limit their interactions before forming a Christmas bubble, that they should think carefully before mixing with elderly or at-risk relatives, and that where possible people should stay local and avoid travel.
Leaders are still trying to strike a balance between allowing people to visit relatives who they may not have seen for months, without allowing the virus to run rampant.
But many still believe that relaxing rules just as many areas are seeing a significant increase in cases is too risky, and will lead to a considerably more difficult period at the start of next year.
The resumption of talks comes as nearly 10.8 million people joined tier-3 Covid restrictions on Wednesday.
It means some 34 million people in England are now living under the toughest rules.
Under the tier three – very high alert – rules, pubs and restaurants must close, except for takeaway and delivery, and indoor entertainment venues such as theatres, bowling alleys and cinemas must remain shut.
Ministers are also due to formally review what tiers in England are appropriate for each area later.
On Tuesday, the Scottish Government announced that three council areas – Aberdeen, Aberdeenshire and East Lothian – are to have tougher coronavirus restrictions imposed from Friday in a bid to reverse rising numbers of cases.
It was also announced that a further 506 people had died within 28 days of testing positive for Covid-19, bringing the UK total to 64,908. Another 18,450 infections were also confirmed in labs.